Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #4537 |
| automorphism | Aut(G) = C22×D3×#120 (order 768) · Inn(G) = #217 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #328 |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,6)(5,8)(7,11)(9,10)(12,13,15,17)(14,18,19,16);(2,3)(4,5)(6,10,11,8)(7,9)(13,16,17,18)Polycyclic presentation:
2^6,3|a^2=c,b^2=f,d^2=f,b^a=bd,d^a=def,g^a=g^2,c^b=ce,d^b=df33 conjugacy classes — view the full character table.
| maximal subgroup of | #68308, #68309, #68310, … |
| maximal normal subgroup of | #68308, #68309, #68310, … |
| maximal quotient of | #67624, #67638, #67642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 97);